Fraction of a Number Formula

The Formula

\frac{a}{b} \times n = \frac{a \times n}{b}

When to use: \frac{3}{4} of 20 means split 20 into 4 equal groups (5 each), then take 3 groups: 3 \times 5 = 15.

Quick Example

\frac{3}{4} \times 20 = \frac{3 \times 20}{4} = \frac{60}{4} = 15

Notation

\frac{a}{b} of n means \frac{a}{b} \times n; the word 'of' translates to multiplication

What This Formula Means

Finding a fraction of a number means multiplying that number by the fraction: \frac{a}{b} of n equals \frac{a}{b} \times n = \frac{a \times n}{b}. It answers 'what is this part of the whole amount?'

\frac{3}{4} of 20 means split 20 into 4 equal groups (5 each), then take 3 groups: 3 \times 5 = 15.

Formal View

For n \in \mathbb{R} and fraction \frac{a}{b}, the quantity '\frac{a}{b} of n' is defined as \frac{a}{b} \cdot n = \frac{an}{b}.

Worked Examples

Example 1

easy
Find \frac{3}{4} of 28.

Solution

  1. 1
    Divide by the denominator first: 28 \div 4 = 7.
  2. 2
    Multiply by the numerator: 7 \times 3 = 21.
  3. 3
    Alternatively: \frac{3}{4} \times 28 = \frac{3 \times 28}{4} = \frac{84}{4} = 21.

Answer

21
Finding a fraction of a number is multiplication: 'of' means multiply. A practical two-step method is to divide by the denominator first (to find one equal part) and then multiply by the numerator (to count the required parts).

Example 2

medium
A school has 360 students. \frac{5}{9} of them play a sport. How many students play a sport?

Common Mistakes

  • Dividing by the numerator instead of the denominator
  • Adding the fraction to the number instead of multiplying
  • Forgetting to multiply by the numerator after dividing by the denominator

Why This Formula Matters

Used constantly in real life—discounts, recipes, dividing quantities, and probability.

Frequently Asked Questions

What is the Fraction of a Number formula?

Finding a fraction of a number means multiplying that number by the fraction: \frac{a}{b} of n equals \frac{a}{b} \times n = \frac{a \times n}{b}. It answers 'what is this part of the whole amount?'

How do you use the Fraction of a Number formula?

\frac{3}{4} of 20 means split 20 into 4 equal groups (5 each), then take 3 groups: 3 \times 5 = 15.

What do the symbols mean in the Fraction of a Number formula?

\frac{a}{b} of n means \frac{a}{b} \times n; the word 'of' translates to multiplication

Why is the Fraction of a Number formula important in Math?

Used constantly in real life—discounts, recipes, dividing quantities, and probability.

What do students get wrong about Fraction of a Number?

Students confuse 'fraction of' with 'fraction plus'—\frac{1}{3} of 12 is 4, not 12\frac{1}{3}.

What should I learn before the Fraction of a Number formula?

Before studying the Fraction of a Number formula, you should understand: multiplying fractions.

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